Q. If the mean of the set of numbers $x_{1},x_{2},\ldots x_{n}$ is $\overline{x}$, then the mean of the numbers $x_{i} + 2i,\ 1 \leq i \leq n$ is
A) $\overline{x} + 2n$
B) $\overline{x} + 2$
C) $\overline{x} + n + 1$
D) $\overline{x} + n$
Explanation
(c)
Mean $= \frac{\sum_{i = 1}^{n}{(x_{i} + 2i)}}{n} = \frac{\sum_{i = 1}^{n}{x_{i} + 2(1 + 2 + ... + n)}}{n}$
$\overline{x} + \frac{2n(n + 1)}{2n} = \overline{x} + (n + 1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.